The minor intervals are not minor because they are found in the minor scale and the same goes for major intervals. The intervals are concepts based on the distance between two notes based on letter name and absolute distance in semitones.
It should also be noted that the term major and minor is used a lot in music and when applied to interval major means further in distance and minor means smaller. In some ways, you can view a minor interval as a half step or semitone above the previous interval set and a major interval as a whole step or tone above the previous interval.
To better explain why the intervals ended up this way, let's look at this solely from a distance perspective at first. The distances from unison to octave are as follows in semitones:
0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12
In C these notes would map to:
C - Db - D - Eb - E - F - F#/Gb - G - Ab - A - Bb - B - C
As you can see, both 0 and 12 map to C and the furthest you could be away from a C in semitones is 6. This leaves us with 5 notes on each side with 1 - 2 - 3 - 4 - 5 closer to 0 and 7 - 8 - 9 - 10 - 11 closer to 12.
Now let's look at the standard interval names. In this I will use M for major, m for minor, P for Perfect and tt for tritone (which is considered both an augmented 4th and a diminished 5th).
P1 - m2 - M2 - m3 - M3 - P4 - tt - P5 - m6 - M6 - m7 - M7 - P8
Now looking at the whole interval spectrum, we notice
- The tritone (or 6 semitones away) has a perfect interval above and below (P4 - tt - P5) and can be described as both an A4 and d5 for this reason.
- The note you are basing the name off of (C in this case which is both 0 and 12) is also perfect (P1 for unison P8 for octave) .
- The other notes are group into twos (because of the two semitones typical max in scales) with the smaller one being minor and the bigger one being major (m2 - M2 - m3 - M3) and (m6 - M6 - m7 - M7).
- The augmented and diminished intervals of the major and minor intervals are for when one of the intervals stretches out of its typical designation.
So in short, a major interval just means it's the bigger of a set of two possible intervals. The fact that the minor scale uses it is kind of irrelevant in this naming scheme.